Chained Bell Inequality Experiment with High-Efficiency Measurements

TL;DR

This experiment demonstrates a violation of a chained Bell inequality using high-efficiency measurements on two ions, providing strong evidence against local realism and certifying Bell states without assumptions.

Contribution

We experimentally violate a chained Bell inequality with high-efficiency ion measurements and develop a statistical framework to quantify local-realistic fractions without common assumptions.

Findings

Excluded local-realistic models with fractions above 0.327 at 95% confidence

Achieved a stronger violation than traditional CHSH experiments

Provided device-independent certification of Bell states

Abstract

We report correlation measurements on two $^9$Be$^+$ ions that violate a chained Bell inequality obeyed by any local-realistic theory. The correlations can be modeled as derived from a mixture of a local-realistic probabilistic distribution and a distribution that violates the inequality. A statistical framework is formulated to quantify the local-realistic fraction allowable in the observed distribution without the fair-sampling or independent-and-identical-distributions assumptions. We exclude models of our experiment whose local-realistic fraction is above 0.327 at the 95 \% confidence level. This bound is significantly lower than 0.586, the minimum fraction derived from a perfect Clauser-Horne-Shimony-Holt inequality experiment. Furthermore, our data provides a device-independent certification of the deterministically created Bell states.